They face deportation as a result of father Rajasegaren Manikam's kidney condition, which is considered a financial burden on Australia.
But local MP and federal Education Minister Dan Tehan told the Herald Sun that while he did not want to preempt a decision from Immigration Minister David Coleman, the groundswell of community support was working.
"The support for the family by the local community and the way the family has contributed to the community points to a positive outcome," he said.
It's understood the minister indicated a decision could be reached by the end of the week.
'This is our home'
The Rajasegaran family moved to Australia from Singapore seven years ago.
Vanisre Rajasegaran, is now in her final months of year 12 at Brauer College and is a member of the school's student council. She is aspiring to study medicine at university and is supposed to sit her final exams in October.
"This is our home," Vanisre wrote on a Change.org petition has reached more than 71,000 signatures, with a target of 75,000.
Her mother, Premawarthy Balasupramaniam holds a visa sponsored by the Warrnambool City Council.
But to maintain the visa, all of her family members need to meet the same visa conditions.
In 2016 her husband was diagnosed with kidney disease.
A medical officer of the federal government ruled Mr Manikam's condition was "likely to result in a significant cost to the Australian community and prejudice the access of an Australian citizen or permanent resident to health care or community services".
But Mr Manikam said - through lifestyle changes - his health has actually improved since 2016.
The family appealed the decision to the Administrative Appeals Tribunal, but it was dismissed. And as a result, the family was given 28 days to leave the country.
They have now been appealing to Mr Coleman for a ministerial intervention.
Speaking to SBS News last week, Ms Balasupramaniam said "what we've built up for seven years, just to give up in 28 days, I just felt that's not fair".
"We've not been heard."